In a large saucepan over medium heat, cook the onion in 1 tablespoon of water, stirring, occasionally, until it begins to soften, about 4 minutes. Add the squash and cook, stirring occasionally, until soft, about 10 minutes.
Add the peeled apples, salt, cumin, coriander, ginger, pepper, and broth. Add extra water if needed to cover the squash and apples. Bring the soup to a boil. Reduce it to a simmer, cover, and cook until the squash and apples are very soft, about 30 minutes.
Purée the soup in batches in a blender or food processor until smooth, and return it to the saucepan. Heat the soup over low, thinning with more water if necessary. Serve with diced apples and jalapeño slices, if you like.
NOTE: This soup can be made ahead of time and refrigerated up to 3 days or frozen up to a month; let cool completely before storing in an airtight container. Reheat gently before serving (thaw frozen soup overnight in the refrigerator).